In this paper, we characterize planarity and outer planarity of complement of graph domination graphs and provide a MATLAB program for identifying graph domination graphs.

Yamuna M

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Elakkiya A

Fulltext

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

International Journal of Engineering & Technology

Subdividing an edge in the graph may increase the domination number or remains the same. In this paper, we introduce a new kind of graph called non - domination subdivision stable graph (NDSS). We obtain a necessary and sufficient condition for a graph to be NDSS. We provide a constructive characterization of NDSS trees and a MATLAB program for identifying NDSS graphs. © Published under licence by IOP Publishing Ltd.

IOP Conference Series: Materials Science and Engineering

Non - domination subdivision stable graphs

Planar graph characterization is always of interest due to its complexity in characterization. In this paper, we obtain a necessary and sufficient condition for a graph to be NDSS and hence characterize the planarity and outer - planarity of its complement G. © Published under licence by IOP Publishing Ltd.

Planar graph characterization of NDSS graphs

A graph G = ( V, E ) is uniquely colorable if the chromatic number χ ( G ) = n and every n - coloring of G induces the same partition of V. Uniquely colorable graphs whose chromatic partition contains at least one γ - set is γ - uniquely colorable graphs In this paper, we characterize the planarity of γ - uniquely colorable graphs. © Published under licence by IOP Publishing Ltd.

Journal	International Journal of Engineering & Technology
Publisher	Science Publishing Corporation
Open Access	Yes